IXL - Find probabilities using the binomial distribution (Algebra 2 practice)

Data scientists studying online safety recently claimed that

32%

of users over age 40 have an email password containing the user's actual name.

Assuming these findings are accurate, if 3 email passwords of users over age 40 are selected at random, what is the probability that exactly 2 of the passwords contain the users' actual names?

Write your answer as a decimal rounded to the nearest thousandth.

ref_doc_title.

Learn with an example

question

Victoria and Julian are designing a basketball launcher. When they launch a basketball from the top of the three-point line, the ball goes in the hoop

19%

of the time.

If they launch 4 basketballs from the three-point line, what is the probability that exactly 3 will go in the hoop?

Write your answer as a decimal rounded to the nearest thousandth.

key idea

A binomial experiment consists of identical and independent trials. In each trial there are two outcomes: success and failure.

In a binomial experiment, the number of successes is a random variable. Its probability distribution is called the binomial

distribution.

The binomial distribution depends on

the number of trials, and

the probability of success. The probability of exactly

successes is:

(

)

(

–

)

–

Sometimes 1 -

the probability of failure, is written as

(

)

–

solution

Interpret the situation as a binomial experiment.

Identify the trials.

A trial is launching a basketball.

Identify a success.

A trial is a success if the basketball goes into the hoop. It is a failure if it does not go in the hoop.

Find the probability.

The question describes a binomial experiment in which the number of trials is 4, the probability of success is 0.19, and the probability of failure is

–

0.19

0.81

Find the probability of exactly 3 successes using a binomial distribution with

0.19

and

0.81

(

)

–

0.19

0.81

–

0.006859

0.81

0.02222316

To the nearest thousandth,

(

)

≈

0.022

Looking for more? Try this:

$Confetti$

Excellent!

Now entering the Challenge Zone—are you ready?

Questions
answeredQuestions

Time
elapsedTime

hr	min	sec
00	00	06

SmartScore
out of 100
IXL's SmartScore is a dynamic measure of progress towards mastery, rather than a percentage grade. It tracks your skill level as you tackle progressively more difficult questions. Consistently answer questions correctly to reach excellence (90), or conquer the Challenge Zone to achieve mastery (100)! Learn more

Teacher tools

Work it out

Not feeling ready yet? These can help:

OO.3Combinations and permutations

PP.3Write a discrete probability distribution

Excellent! You got that right!

Jumping to level 1 of 1

Excellent!